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13.3 Surface Durability

The Lewis formula and its modification to Incorporate dynamic conditions is limited to beam-stress analysis. In addition, there are stresses generated in the surface layers of the teeth by the direct crushing action of the forces. These stresses can exceed the material limits and can result in pitting, scoring, scuffing, seizing and plastic deformation.

Pitting — This is the removal of small bits of metal from the surface, due to fatigue, thereby leaving small holes or pits. This is caused by high tooth loads leading to excessive surface stress, a high local temperature due to high rubbing speeds, or inadequate lubrication. Minute cracking of the surface develops, spreads and ultimately results in small bits breaking out of the tooth surface.

Scoring — This is a heavy scratch pattern extending from tooth root to tip. It appears as if a heavily-loaded tooth pair has dragged foreign matter between sliding teeth. It can be caused by lubricant failure, incompatible materials and overload.

Scuffing — This is a surface destruction composed of plastic material flow plus superimposed gouges and scratches caused by loose metallic particles acting as an abrasive between teeth. Both scoring and scuffing are associated with welding (or seizing) and plastic deformation. Frequently it is difficult to distinguish among the several types of failure as there is considerable intermingling.

There have been many attempts to derive expressions for calculating safe surface stress. The Buckingham durability equations based on Hertzian contact stresses and the work of others can be found in the references. All of the various design equations and procedures are closely related to specific empirical data and experience. The AGMA equations are in wide use in the United States.

13.4 AGMA Strength and Durability Ratings

The AGMA rating formulas again represent a combinations of analysis, approximations, and empirical data. A complete treatment of AGMA practices is too extensive for this discussion and only an introductory survey is offered. More details are available from AGMA literature and Chapter 11 of Reference 6.

The AGMA formulas pertain to strength and surface durability, with dynamic and other effects induded. The equations are:

Tooth Strength (bending stress):

St = WtKo .  Pd   .   KsKm                                                           (58) 
        Kv         F        J
 
Surface Durability:       
        
Sc = Cp    WtCo .  Cs   .   CtCm                                                           (59) 
               Cv      dF           l        

These equations relate stress to load, size and stress parameters.
The calculated stresses must be less than the allowable stress values of the material, which in turn depend on the nature of the application. The allowable stresses are as follows:

Allowable surface durability stress:

St =< Sat KL                                                             (60)
             KrKr

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